Gabriela is 16 years older than Ben. Sixteen years ago, Gabriela was 3 times as old as Ben. How old is Ben now?
Solution: We can use the given information to write down two equations that describe the ages of Gabriela and Ben. Let Gabriela's current age be $g$ and Ben's current age be $b$ The information in the first sentence can be expressed in the following equation: $g = b + 16$ Sixteen years ago, Gabriela was $g - 16$ years old, and Ben was $b - 16$ years old. The information in the second sentence can be expressed in the following equation: $g - 16 = 3(b - 16)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $b$ , it might be easiest to use our first equation for $g$ and substitute it into our second equation. Our first equation is: $g = b + 16$ . Substituting this into our second equation, we get the equation: $(b + 16)$ $-$ $16 = 3(b - 16)$ which combines the information about $b$ from both of our original equations. Simplifying both sides of this equation, we get: $b + 0 = 3 b - 48$ Solving for $b$ , we get: $2 b = 48$ $b = 24$.